Browsing by Author "van 't Wout, Elwin"

Now showing 1 - 6 of 6
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    Accelerating frequency-domain numerical methods for weakly nonlinear focused ultrasound using nested meshes
    (2021) Groth, Samuel P.; Gelat, Pierre; Haqshenas, Seyyed R.; Saffari, Nader; van 't Wout, Elwin; Betcke, Timo; Wells, Garth N.
    The numerical simulation of weakly nonlinear ultrasound is important in treatment planning for focused ultrasound (FUS) therapies. However, the large domain sizes and generation of higher harmonics at the focus make these problems extremely computationally demanding. Numerical methods typically employ a uniform mesh fine enough to resolve the highest harmonic present in the problem, leading to a very large number of degrees of freedom. This paper proposes a more efficient strategy in which each harmonic is approximated on a separate mesh, the size of which is proportional to the wavelength of the harmonic. The increase in resolution required to resolve a smaller wavelength is balanced by a reduction in the domain size. This nested meshing is feasible owing to the increasingly localised nature of higher harmonics near the focus. Numerical experiments are performed for FUS transducers in homogeneous media to determine the size of the meshes required to accurately represent the harmonics. In particular, a fast volume potential approach is proposed and employed to perform convergence experiments as the computation domain size is modified. This approach allows each harmonic to be computed via the evaluation of an integral over the domain. Discretising this integral using the midpoint rule allows the computations to be performed rapidly with the FFT. It is shown that at least an order of magnitude reduction in memory consumption and computation time can be achieved with nested meshing. Finally, it is demonstrated how to generalise this approach to inhomogeneous propagation domains.
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    Frequency-robust preconditioning of boundary integral equations for acoustic transmission
    (2022) van 't Wout, Elwin; Haqshenas, Seyyed R.; Gelat, Pierre; Betcke, Timo; Saffari, Nader
    The scattering and transmission of harmonic acoustic waves at a penetrable material are commonly modelled by a set of Helmholtz equations. This system of partial differential equations can be rewritten into boundary integral equations defined at the surface of the objects and solved with the boundary element method (BEM). High frequencies or geometrical details require a fine surface mesh, which increases the number of degrees of freedom in the weak formulation. Then, matrix compression techniques need to be combined with iterative linear solvers to limit the computational footprint. Moreover, the convergence of the iterative linear solvers often depends on the frequency of the wave field and the objects' characteristic size. Here, the robust PMCHWT formulation is used to solve the acoustic transmission problem. An operator preconditioner based on on surface radiation conditions (OSRC) is designed that yields frequency-robust convergence characteristics. Computational benchmarks compare the performance of this novel preconditioned formulation with other preconditioners and boundary integral formulations. The OSRC preconditioned PMCHWT formulation effectively simulates large-scale problems of engineering interest, such as focused ultrasound treatment of osteoid osteoma.(c) 2022 Elsevier Inc. All rights reserved.
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    Modeling frequency shifts of collective bubble resonances with the boundary element method
    (2023) Jerez Boudesseul, Rudyard; van 't Wout, Elwin
    Increasing the number of closely packed air bubbles immersed in water changes the frequency of the Minnaert resonance. The collective interactions between bubbles in a small ensemble are primarily in the same phase, causing them to radiate a spherically symmetric field that peaks at a frequency lower than the Minnaert resonance for a single bubble. In contrast, large periodic arrays include bubbles that are further apart than half of the wavelength such that collective resonances have bubbles oscillating in opposite phases, ultimately creating a fundamental resonance at a frequency higher than the single-bubble Minnaert resonance. This work investigates the transition in resonance behavior using a modal analysis of a mass-spring system and a boundary element method. The computational complexity of the full-wave solver is significantly reduced to a linear dependence on the number of bubbles in a rectangular array. The simulated acoustic fields confirm the initial downshift in resonance frequency and the strong influence of collective resonances when the array has hundreds of bubbles covering more than half of the wavelength. These results are essential in understanding the low-frequency resonance characteristics of bubble ensembles, which have important applications in diverse fields such as underwater acoustics, quantum physics, and metamaterial design.
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    Proximity resonances of water-entrained air bubbles near acoustically reflecting boundaries
    (2021) van 't Wout, Elwin; Feuillade, Christopher
    The acoustic resonances of radiatively damped air bubbles in water near reflecting boundaries are investigated by representing the bubble and its image by two bubbles in a full space, ensonified by two incident fields. Results obtained using an analytic monopole theory are compared with those of a coupled spherical harmonic technique and a boundary element method. Near a rigid boundary, the resonance frequency is reduced, and the response characteristics are determined by the predominant monopolar character of the individual bubble motion, with small changes in peak amplitude and Q. Near a sound-soft boundary, a higher frequency proximity resonance is observed. The monopole field is cancelled out, and the response is determined by higher-order scattering modes, giving very high values of Q. While the individual bubble scattering level increases significantly, the overall scattering is less than for two uncoupled bubbles. For bubble separations of 8-28 radii, all three approaches predict essentially identical results for both boundary types. For bubble separations less than one radius, the monopole theory, which does not include higher-order scattering modes, diverges from the boundary element and coupled spherical harmonic methods, whose high-accuracy determinations of resonance frequencies and amplitudes agree to within 0.1%.
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    Stable and efficient FEM-BEM coupling with OSRC regularisation for acoustic wave transmission
    (2022) van 't Wout, Elwin
    The finite element method (FEM) and the boundary element method (BEM) can numerically solve the Helmholtz system for acoustic wave propagation. When an object with heterogeneous wave speed or density is embedded in an unbounded exterior medium, the coupled FEM-BEM algorithm promises to combine the strengths of each technique. The FEM handles the heterogeneous regions while the BEM models the homogeneous exterior. Even though standard FEM-BEM algorithms are effective, they do require stabilisation at resonance frequencies. One such approach is to add a regularisation term to the system of equations. This algorithm is stable at all frequencies but also brings higher computational costs. This study proposes a regulariser based on the on-surface radiation conditions (OSRC). The OSRC operators are also used to precondition the boundary integral operators and combined with incomplete LU factorisations for the volumetric weak formulation. The proposed preconditioning strategy improves the convergence of iterative linear solvers significantly, especially at higher frequencies. (C) 2021 Elsevier Inc. All rights reserved.
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    The boundary element method for acoustic transmission with nonconforming grids
    (2024) van 't Wout, Elwin
    Acoustic wave propagation through a homogeneous material embedded in an unbounded medium can be formulated as a boundary integral equation and accurately solved with the boundary element method. The computational efficiency deteriorates at high frequencies due to the increase in mesh size with a fixed number of elements per wavelength and also at high material contrasts due to the ill -conditioning of the linear system. This study presents the design of boundary element methods feasible for nonconforming surface meshes at the material interface. The nonconforming algorithm allows for independent grid generation, improves flexibility, and reduces the degrees of freedom. It works for different boundary integral formulations for Helmholtz transmission problems, operator preconditioning, and coupling with finite element solvers. The extensive numerical benchmarks at canonical configurations and an acoustic foam model confirm the significant improvements in computational efficiency when employing the nonconforming grid coupling in the boundary element method.